Involve: A Journal of Mathematics

  • Involve
  • Volume 2, Number 2 (2009), 225-236.

Congruences for Han's generating function

Dan Collins and Sally Wolfe

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For an integer t1 and a partition λ, we let t(λ) be the multiset of hook lengths of λ which are divisible by t. Then, define ateven(n) and atodd(n) to be the number of partitions of n such that |t(λ)| is even or odd, respectively. In a recent paper, Han generalized the Nekrasov–Okounkov formula to obtain a generating function for at(n)=ateven(n)atodd(n). We use this generating function to prove congruences for the coefficients at(n).

Article information

Involve, Volume 2, Number 2 (2009), 225-236.

Received: 29 September 2008
Accepted: 17 January 2009
First available in Project Euclid: 20 December 2017

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Zentralblatt MATH identifier

Primary: 05A17: Partitions of integers [See also 11P81, 11P82, 11P83] 11P83: Partitions; congruences and congruential restrictions

partition partition function Han's generating function Nekrasov–Okounkov hook length Ramanujan congruences congruences modular forms


Collins, Dan; Wolfe, Sally. Congruences for Han's generating function. Involve 2 (2009), no. 2, 225--236. doi:10.2140/involve.2009.2.225.

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